lec1 - Data Analysis for Financial Engineers Professor S....

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Data Analysis for Financial Engineers Professor S. Kou Department of IEOR, Columbia University Lecture 1a. Introduction 1 What is this course about? Data Analysis for FE: Time Series (AR, MA, ARMA, ARCH, GARCH) Regression (Time series regression) Empirical Finance. (Capital Asset Pricing Model, fac- tor Models, e cient market hypothesis, continuous time models) 2 Applications. 1. Hedging & Risk Management 2. Program Trading In the classical Black-Scholes model, it is assumed that the dynamics of the stock prices is given by ( )= (0) exp {  +  ( ) } where ( ) is a standard Brownian motion. 3 After we have such wonderful models, why do we need to learn Data Analysis? Three reasons: (1) Test whether models f t data. (2) Estimate parameters in the models. (3) Build new Mathematical/Statistical models. For exam- ple, alternative models to the Black-Scholes model. 4
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Dow Jones Index On Oct 19, 1987, Monday, the DJ Industrial Average fell by 25.6%. From Jan 1, 1980 to Oct 16, 1987, Friday, the standard deviation of daily returns on the Dow was about 1.16%. The drop of 25.6% was about a negative return of 22 standard deviations, after re-centering the mean of the daily return (which is close to zero). 5 If the Black-scholes model is correct, then the stock return will have a normal distribution. ( ≤− 22) = Φ ( 22) = 1 4 10 107 The universe is believed to have existed for 15 billion years or about 5 10 17 seconds. 6 Mathematics will be used in this course includes: 1. Intro to Statistics. 2. Some optimization tools. 3. S-plus programming language 7 What are S-Plus and S+FinMetrics? S was originally developed at Bell Labs. S was bought by Insightful Corporation and became S-Plus. FinMetrics was added to S-Plus around 2000. It mainly deals with f nancial time series, including GARCH models and time series regression. 8
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Students are responsible to get the necessary software pack- ages. (Just like the textbook requirement). Inquire about how to get S-Plus and FinMetrics should be addressed to www.insightful.com Di f erences between S-Plus and other software packages, such as R, SAS, Matlab, etc. 9 Review of Basic Statistics 1. Random Variables Discrete: binomial, Poisson,. .. Continuous: normal, exponential, gamma, 2 ,. . . 10 S-plus commands: rnorm: generating N(0,1) rpois: generating Poisson random variables help(rnorm): ask for help in S-plus. normal density: S-plus commend: dnorm Cumulative distribution function (cdf): ( )= ( ) The cdf of N(0,1) is given by Φ ( Z −∞ ( )  11 S-plus: pnorm 12
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2 , and distributions Suppose , =1 2   are standard normal random vari- ables. Then X =1 2 2 the chi-squared distribution with d.f. . = p 2  13 1  2 = 2 1  1 2 2  2 14 Expectation: discrete: ( )= P  ( = ) continuous: ( R −∞  ( )  Variance  ( [( ( )) 2 ]= [ 2 ] ( [ ]) 2 Standard deviation:  (
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lec1 - Data Analysis for Financial Engineers Professor S....

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